Investigation for the k-analogue of τ-Gauss hypergeometric matrix functions and associated fractional calculus

Abstract

In this manuscript, we present a new definition of ( k , τ ) -Gauss hypergeometric matrix function and study its analytical properties, like derivative formulas and integral representations. Furthermore, as an application we establish k -fractional calculus operators for the novel matrix function. We also give some new and known results as special cases of our proposed generalization of the Wright hypergeometric matrix function.